This is an open-label, randomized, multicenter study of FPI-2265 (225Ac-PSMA-I&T). Patient population is adult participants with PSMA positive mCRPC who have had previous treatment with with 177Lu-PSMA-617 or another 177Lu-PSMA radioconjugate (RC). The purpose of the study is to determine the safety and tolerability, and recommended dose and regiment of FPI-2265.

This is an open-label, randomized, multicenter study of FPI-2265 (225Ac-PSMA-I&T). The purpose of this dose optimization study is to determine the recommended FPI-2265 dose and regimen. Conclusions will be based on safety, tolerability, and anti-tumor activity.

Screening Period: At screening, participants will be assessed for eligibility and undergo a positron emission tomography (PET)/computed tomography (CT) scan to evaluate PSMA positivity. Only participants with PSMA positive cancer and confirmed eligibility criteria will be randomized.

Participants randomized will enter the treatment period and receive investigational doses of FPI2265 according to the dose level and schedule as specified per proposed dose arm.

Part A participants will enroll 1:1:1 at three dose level/schedules, to arms 1, 2 or 3

Part B participants will enroll after completion of part A, in a 1:1 randomization scheme to arms 6 or 7.

Once Part A is fully enrolled and participants have been followed for at least 12 weeks, data from Arm 1 and 2 will be analyzed to assess the feasibility of enrolling participants to arms 4 and 5.

All participants will be monitored and assessed for efficacy response, disease progression and adverse events.

Supportive care will be allowed in all arms at the discretion of the investigator and includes available care for the eligible participant according to best institutional practice for mCRPC treatment, including androgen deprivation therapy (ADT).

Follow-up after end of treatment visit will proceed for 5 years.

5 participants will be enrolled into a dosimetry substudy (open at select sites only). Dosimetry substudy participants will be administered one dose at of FPI2265 and proceed with dosimetric assessments will be taken at a number of timepoints after dose administration.

Key Inclusion Criteria:

• Eastern Cooperative Oncology Group (ECOG) Performance Status 0 or 1
• Diagnosis of adenocarcinoma of prostate proven by histopathology.
• Must have had prior orchiectomy and/or ongoing androgen-deprivation therapy and a castrate level of serum/plasma testosterone
• Progressive mCRPC at time of study entry.
• Must have been previously treated with lutetium-PSMA therapy (lutetium-177 vipivotide tetraxetan or other lutetium-177-PSMA RLT). Treatment must have been completed >6 weeks prior to the first dose of study drug.
• Participants with known BRCA mutations should have received FDA-approved therapies such as PARP inhibitors, per Investigator discretion.
• Positive PSMA PET/CT scan
• Adequate organ function
• For participants who have partners of childbearing potential: Partner and/or participant must not be planning to conceive and must use a method of birth control with adequate barrier protection deemed acceptable by the Principal Investigator during the study treatment and for six months after last study drug administration.

Key Exclusion Criteria:

• Participants who received more than two prior lines of cytotoxic chemotherapy for CRPC.
• Participants who progress prior to administration of the 3rd cycle of prior treatment with 177Lu-PSMA therapy
• All prior treatment-related adverse events must have resolved to Grade ≤1 (CTCAE v5.0). Alopecia and stable persistent Grade 2 peripheral neuropathy may be allowed at the discretion of the Investigator.
• Participants with known, unresolved, urinary tract obstruction are excluded.
• Administration of any systemic cytotoxic or investigational therapy ≤30 days of the first dose of study treatment or five half-lives, whichever is shorter. Completion of large-field external beam radiotherapy ≤four weeks of the first dose of study treatment.
• Participants with a history of central nervous system (CNS) metastases are excluded except those who have received therapy
• Participants with any liver metastases will be excluded
• Participants with skeletal metastases presented as a superscan on a ⁹⁹ᵐTc bone scan.
• Previous or concurrent cancer that is distinct from the cancer under investigation in primary site or histology, except treated cutaneous basal cell carcinoma or squamous cell carcinoma and superficial bladder tumors. Any cancer curatively treated >two years prior to the first dose of treatment is permitted.
• Concurrent serious (as determined by the investigator) medical conditions
• Major surgery ≤30 days prior to the first dose of study treatment.